Collision number typical

A typical value of the collision number is 10 °s in gases at one atmosphere pressure and room temperature, and the number of successful collisions which can bring about the chemical reaction is equal to this number multiplied by the Anhenius or probability factor, exp(— /f 7 ), where E is the activation energy, the critical collision energy needed for reaction to occur. 

Microkinetic modeling assembles molecular-level information obtained from quantum chemical calculations, atomistic simulations and experiments to quantify the kinetic behavior at given reaction conditions on a particular catalyst surface. In a postulated reaction mechanism the rate parameters are specified for each elementary reaction. For instance adsorption preexponential terms, which are in units of cm3 mol"1 s"1, have been typically assigned the values of the standard collision number (1013 cm3 mol"1 s 1). The pre-exponential term (cm 2 mol s 1) of the bimolecular surface reaction in case of immobile or moble transition state is 1021. The same number holds for the bimolecular surface reaction between one mobile and one immobile adsorbate producing an immobile transition state. However, often parameters must still be fitted to experimental data, and this limits the predictive capability that microkinetic modeling inherently offers. A detailed account of microkinetic modelling is provided by P. Stoltze, Progress in Surface Science, 65 (2000) 65-150. 

Table 2.2b Speeds and Collision Numbers for Some Typical Gases ...

Typical Rate Constants and Collision Numbers for Energy Transfer... 

In air, the mean-free path has an order of 10 m and does not depend on temperature but is inversely proportional to pressure. The expressions given for collision number and mean-free path are useful for understanding chemical reactions (see collision theory in Chapter 4.1.1.2) but have only limited worth for applications because the molecular diameter (or radius) is not directly measurable. However, the molecular diameter is typically determined from viscosity measurements. 

Initiated by meteorological investigations on formation of rain drops, as well as spray combustion, binary drop collision has been investigated for more than half a century [3-5]. The outcomes of binary droplet collisions are typically summarized in collision maps as shown in Fig. 6.1. The Weber-number measures the ratio of the inertial force to the surface tension force. We = pu d/a, where p is the density, u is the collision velocity, d is the drop diameter, and a is the surface tension. The impact parameter B is a measure of the geometry of drop collisions as illustrated in Fig. 6.1. 

This collision number is in stark contrast to low-energy CID, which typically occurs at much higher pressure ( 10 torr) and can involve as many as 10 collisions in a quadrupole ion trap. 

Figure B2.3.5. Typical time-of-flight spectra of DF products from the F + D2 reaction [28]- The collision energies and in-plane and out-of-plane laboratory scattered angles are given in each panel. The DF product vibrational quantum number associated with each peak is indicated. Reprinted with pennission from Faiibel etal [28]. Copyright 1997 American Chemical Society.

Typical events that are considered are fire, explosion, ship collision, and the failure of pressurized storage vessels for which historical data established the failure frequencies. Assessment of consequences was based partly on conservative treatment of past experience. For example ilic assessment of the number of casualties from the release of a toxic material was based on past histoiy conditioned by knowledge of the toxicology and the prevailing weather conditions. An altemati. e used fault trees to estimate probabilities and identify the consequences. Credit is taken in this process for preventative measures in design, operation, and maintenance procedures. Historical data provide reliability expected from plant components and humans. 

This argument is based upon the typical situation in which E is well out on the tail of the curve. Suppose it is not suppose E is near the maximum of the curve at 7i, or is even to the left of it. Then a large number of the molecules have the requisite energy, even at the lower temperature, Tt. Since collisions occur so rapidly (remember, one every 10 s second or so), the reaction is over in a blink of the eye. This reaction would be called instantaneous." The circumstances shown in Figure 8-4 are typical" only of a slow reaction. 

Collision theory is mute about the value of fji. Typically,1, so that the number of molecules colliding is much greater than the number reacting. See Problem 1.2. Not all collisions have enough energy to produce a reaction. Steric effects may also be important. As will be discussed in Chapter 5, fji is strongly dependent on temperature. This dependence usually overwhelms the dependence predicted for the collision rate. 

The number of surface collisions at p=l bar and T = 300 K is thus rcoii-surf = 1-08 X 10 m s for hydrogen and 2.88 x 10 m s for nitrogen. Since there are typically 1.5 x 10 surface atoms per m, a surface atom will on average be hit a billion times per second under ambient conditions. This, however, does not necessarily mean that the gas molecule reacts, particularly if the reaction is an activated process. 

In a silane-hydrogen discharge the feedstock gases SiHa and H2 take part in all the processes that occur. A large number of reactions have been proposed (see e.g. Kushner [190]). Nienhuis et al. [191] have performed a sensitivity analysis in their self-consistent fluid model, from which a minimum set of reactions have been extracted for a typical low-pressure RF discharge. Tables II and III list these reactions. They will be used in the plasma models described in subsequent sections. The review articles on silane chemistry by Perrin et al. [192] and on hydrogen by Phelps [193] and Tawara et al. [194] have been used. The electron collision data are compiled in Figure 13 [189]. 

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